Suppose that  $a$ and $b$ are digits, not both nine and not both zero, and the repeating decimal  $0.\overline{ab}$ is expressed as a fraction in lowest terms. How many different denominators are possible?
Since $0.\overline{ab} = \frac{ab}{99}$, the denominator must be a factor of $99 = 3^2 \cdot 11$. The factors of $99$ are $1,$ $3,$ $9,$ $11,$ $33,$ and  $99$. Since $a$ and $b$ are not both nine,  the denominator cannot be $1$. By choosing $a$ and $b$ appropriately,  we can make fractions with each of the other denominators.

Thus, the answer is $\boxed{5}$.